What is the period of the function $$y=\tan(kx)$$ ?

The period of the tangent function is given by $$\frac{\text{π}}{k}$$ .

What is the period of the function $$y=\tanigg(\frac{4}{3}tigg)$$ ?

The period is $$\frac{3\text{π}}{4}$$ .

What is the period of the function $$y=2\text{cot}(2x)+1$$ ?

The period is $$\frac{\text{π}}{2}$$ .

Identify the vertical asymptote of the function $$y=\text{cot}(2(x+\frac{\text{π}}{3}))$$ .

The vertical asymptote is located at $$x = -\frac{\text{π}}{3}$$ .

What is the range of the cotangent function?

The range of the cotangent function is all real numbers, i.e., $$(-\text{∞}, \text{∞})$$ .

What is the range of the tangent function?

The range of the tangent function is all real numbers, i.e., $$(-\text{∞}, \text{∞})$$ .

What is the x-intercept of the function $$y=\tan(x)$$ ?

The x-intercept occurs at $$x = n\text{π}$$ for integer n.

What is the y-intercept of the function $$y=\tan(x)$$ ?

The y-intercept occurs at $$y = 0$$ when $$x = 0$$ .

What is the period of the cotangent function?

The period of the cotangent function is $$\text{π}$$ .

How do you find the period of a transformed tangent function?

For a function of the form $$y=\tan(kx)$$ , the period is calculated as $$\frac{\text{π}}{k}$$ .

What is the effect of a vertical shift on the tangent function?

A vertical shift moves the graph up or down without affecting the period or asymptotes.

What is the effect of a horizontal shift on the cotangent function?

A horizontal shift moves the graph left or right, affecting the location of the vertical asymptotes.

Flashcard 2 (Trig Unit 2) - Tangent & Cotangent RETAKE Flashcards

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1.

FLASHCARD QUESTION

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2.

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3.

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4.

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What are vertical asymptotes in the context of cotangent functions?

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5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

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What is the general form of the cotangent function?

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7.

FLASHCARD QUESTION

Front

What is the difference between tangent and cotangent functions?

Back

Tangent is the ratio of sine to cosine, while cotangent is the ratio of cosine to sine.

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